Overlappingly overstrikeable ribbons for matrix printing systems with a carrier film are already known. The carrier film is made from a plastic, which can e.g. be of a thermosetting or thermoplastic nature. When using such ribbons in matrix printing systems many different disadvantages are encountered. The needles rapidly cause perforations and deformations which consequently damage the carrier film and make the ribbon unusable, particularly on passing through several times. These disadvantageous effects lead to unsatisfactory clarity or definition. The problem is particularly significant with a newer matrix printing system with a larger number of needles per surface unit and with finer needles.